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Recently I encountered a question, which seems to have since been deleted, that once answered ends in a far too often encountered scenario. I can't recall the name of the OP or the question but the basic idea of the question was:

If $\Phi,\Psi:\mathbb R^n \to\mathbb R^n $ are diffeomorphisms, and $f:\mathbb R\to[0,1]$ is smooth and surjective, is the map $x\mapsto f(\|x\|)\Phi(x)+(1-f(\|x\|))\Psi(x)$ a diffeomorphism?

I promptly posted a counterexample. Within a few minutes, the OP and I engaged in what I have come to identify as a cat and mouse game: they comment on my answer with a slight modification to their question, I reply with a counterexample, they modify, I counter, ad infinitum. When I had my limit, I replied with my latest counterexample, and recommended the OP edit their question to fit the specific question.

This isn't the first time I've been in this scenario, and I imagine others have encountered this as well. And while the mouse may not see this as a bother, the cat can find this situation annoying. So I was wondering:

How one can spot a question that will diverge into this sort of cat and mouse game?

How one can recommend the user edit their question in order to avoid this from happening?

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  • $\begingroup$ There's a similar question here. $\endgroup$ – user99914 Mar 2 '18 at 6:06
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    $\begingroup$ I usually tell the user that I already answered their question and request that they post a new question instead of continually modifying the current one. $\endgroup$ – Qudit Mar 2 '18 at 6:10
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    $\begingroup$ I have found a very small number of users who do this a lot, and I've stopped looking at their questions. $\endgroup$ – Gerry Myerson Mar 2 '18 at 6:12
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    $\begingroup$ This is a judgement call. Sometimes it is easy to see that the asker needs a bit of help in specifying exactly what they are asking. In such a case I am willing to play along at least for a while, fully prepared to be shooting at a moving target. Sometimes that worked well. Sometimes it didn't, and I regretted not restricting myself to a few comments seeking to clarify the question (when it was clear that a key assumption or three was missing). I'm afraid I cannot offer a clear cut piece of advice other than to use your judgment. $\endgroup$ – Jyrki Lahtonen Mar 2 '18 at 7:04
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    $\begingroup$ Perhaps vote to close the question as "unclear what you're asking"? $\endgroup$ – Joel Reyes Noche Mar 2 '18 at 7:05
  • $\begingroup$ @JoelReyesNoche It seems that sometimes the question is clear, but the asker keeps adding extra assumptions so that one has to change the answers repeatedly. Sometimes it is not easy to spot what exactly the asker is really looking for. Indeed even the asker might not know about that when they posted the question. $\endgroup$ – user99914 Mar 2 '18 at 7:26
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    $\begingroup$ @John, if "it is not easy to spot what exactly the asker is really looking for," isn't that the textbook definition of "unclear what you're asking"? $\endgroup$ – Gerry Myerson Mar 2 '18 at 12:03
  • $\begingroup$ @Gerry, I meant to say that some user wanted to prove A, but instead asked B as a question. $\endgroup$ – user99914 Mar 2 '18 at 17:09
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    $\begingroup$ meta.stackexchange.com/questions/66377/what-is-the-xy-problem $\endgroup$ – Asaf Karagila Mar 2 '18 at 19:27
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    $\begingroup$ I have asked such a question : see for example math.stackexchange.com/q/2241608/72031 I interacted with answerers via comments and kept updating the question as my understanding about the question improved. I think this can happen when the question is not coming from a textbook but rather as result of some doubts in your mind especially when you are a novice in the topic concerned. I expect a similar behavior from askers when they are unclear about what they are asking. IMO if you sincerely want to learn there are people here who will help you learn even more sincerely. $\endgroup$ – Paramanand Singh Mar 2 '18 at 20:02
  • $\begingroup$ In general the asker should update the question and not just leave his responses in the comments alone (most users won't read each and every comment simply for lack of time). Otherwise vote for closure. $\endgroup$ – Paramanand Singh Mar 2 '18 at 20:04
  • $\begingroup$ Related (to some extent): What to do about repeatedly changing question? and maybe also Changing the question and invalidating previous answer. (and the posts linked there). $\endgroup$ – Martin Sleziak Mar 3 '18 at 2:27
  • $\begingroup$ At Cross Validated this happens a lot and is seen as necessary, often the main problem of the asker is they do not know how to formulate a statistics question, that is what must be solved. $\endgroup$ – kjetil b halvorsen Mar 8 '18 at 12:18
  • $\begingroup$ If you find it annoying why don’t you just stop commenting / posting on the question? $\endgroup$ – Prince M Mar 11 '18 at 5:15
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I think there are three scenarios which can prompt this:

  1. An incorrect copy of a question from a textbook/notes from a given class.
  2. The XY problem, as Asaf mentions in the comments.
  3. A question which springs independently as curiosity of the user.

Note that they are not mutually disjoint. I will adress your questions for each of the cases.

I think the most easily manageable is number 1. It usually is very easy to spot a typo, and so we only need to ask something like: "are you sure that is what you mean, and not (...)?" If the user is not responsive, then disengage. If the question makes sense with the typo, leave it be (it may become a difficult question/trivial question etc). If the question doesn't make sense, apply "standard procedure": vote to close as whatever best reason you see fit (it most likely will be unclear what is being asked, or lacking context). Furthermore, a typo will probably not lead to a lot of edits (there may be cases where a lot of typos may indeed lead to a lot of edits, but these are rare. I don't recall any instance of this happening).

Number 2 and 3 can be wild beasts. As soon as a "cat and mouse" question begins to surface (i.e., the user has edited/commented sometimes changing it) and it does not look like a typo, I think the best course of action is to try and verify if you are dealing with the XY problem. I think something as simple as commenting "Are you falling in the XY problem? If so, please try to make explicit the question that motivated you, so we can show better ways to get there." If the user acknowledges this, problem solved. If not, then you probably are in case 3 which is the worst in my opinion.

Number 3 has the most potential to be stressful. In this case, the user probably has not a good grasp of what he is asking and will forget "trivial" cases (or treat cases which are not trivial as "trivial" because they are not the kind of thing they expect). Here, I don't think there is a clear-cut procedure. Try and talk with the user, and emphasize that changing a question in such a way that potential answers could be invalidated, even if there are none, is bad. If he is not satisfied with the question he made due to the possible answers then make another, making sure that the question is the right one this time. If the talk is productive, good. But as soon as you realize the talk is not being (or will not be) productive, disengage. If you feel the user is being remarkably rude or disruptive, I think flagging for moderator attention is appropriate. If an edit war begins to happen (people rolling back the question to a previous state but OP not agreeing), flagging also seems appropriate.

Another problem with number 3 is that it may be the case that it is "clear" (also a problem to determine when something is "clear" or not) that OP meant something else, and thus the edit is expected, but people rushed to answer the question for whatever reason. However, this situation will probably be a "one-edit" kind of thing, not several ones. I'm only mentioning this problem for completeness, since I think it is relevant and is one instance where OP has less of the blame.

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    $\begingroup$ I recommend not using the pronoun "he" to refer to a hypothetical user or to a user whose gender is unknown. Defaulting to male pronouns is a symptom of our implicit biases, and using them in these situations also reinforces and perpetuates biases against women in mathematics. $\endgroup$ – Greg Martin Mar 5 '18 at 2:36
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    $\begingroup$ @GregMartin: I'm pretty sure defaulting to male pronouns is a feature of language, not our biases. It may be part of the reason we have such biases, and that may be good enough reason to find ways to avoid it, but it is not itself the product of bias. $\endgroup$ – Excluded and Offended Mar 5 '18 at 19:24
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    $\begingroup$ Many of our current English "rules" are the result of intentional prescriptivist grammar choices made in Victorian England, the main effect of which was to keep the upper class separate from other classes. In other words, "a feature of language" often is actually a cultural construct—and thus very much can be the product of bias. Certainly, some grammatical conventions endure while others do not, and those choices are shaped by culture. I choose to promote an inclusive culture, including which of the competing pronoun conventions I use; it sounds like you might agree :) $\endgroup$ – Greg Martin Mar 5 '18 at 19:51
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    $\begingroup$ @Greg: I am pretty sure the majority of users on this site are not native English speakers, who ultimately have an internal monologue in their own native tongues. I find it borderline offensive to ignore that. Yes, we should be receptive towards inclusion, and we should be making less assumptions on people whose gender is unknown. But for crying out loud, most people here speak English as a foreign language. Cut them some slack, would you? (The point being that other languages have this feature regardless to Victorian preferences.) $\endgroup$ – Asaf Karagila Mar 6 '18 at 8:19
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    $\begingroup$ @Greg: And for what it's worth, when I see someone saying something negative about a hypothetical user and using "she" to address that user, I find it more offensive towards the women of mathematics. $\endgroup$ – Asaf Karagila Mar 6 '18 at 8:22
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    $\begingroup$ To add to Asaf's point, I am Brazilian. Here most nouns have genders associated (for instance, "the user" is o usuário (male) or a usuária (female)) and there is no genderless pronoun, so we use the male one as "indeterminate/unknown" when that is the case. Regardless of the reasons for that, that is how the language is. There are "attempts" to try to circunvent this (there are people who say things like "x usuárix", which would only "work" on a written environment), but trying to change the basis of how a language is structured is very difficult (compare to notation in mathematics). $\endgroup$ – Aloizio Macedo Mar 6 '18 at 8:50
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    $\begingroup$ Aside from that, as an example, if I work at a store and say Tivemos dois clientes hoje (which is "We had two clients today" in a male variant, with female one being Tivemos duas clientes hoje), no brazilian will assume that I had two male clients (unless my store was gender-specific for some reason). $\endgroup$ – Aloizio Macedo Mar 6 '18 at 8:53
  • $\begingroup$ The English language has singular they as an alternative. It felt a bit awkward at first, but I am becoming more comfortable using the construct.Admittedly I still don't know if I'm using it correctly for people are often too polite to correct a foreigner abusing it. $\endgroup$ – Jyrki Lahtonen Mar 15 '18 at 7:31
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How one can spot a question that will diverge into this sort of cat and mouse game?

Difficult to "spot the question", easier to "spot the user". The question will have many obvious errors and assumptions that are obviously going to lead to a big rewrite, but if it doesn't it can be difficult to determine from the question if the user (or anyone else) is going to swoop in and invalidate your answer.

When the change is sufficient, beyond a reasonable refinement, you need to assess who's writing the question the asker or you; the person asking is supposed to be the asker, if you have to rewrite it you might as well do exactly that, or not.

Sometimes it's necessary for a bit of back and forth, but you need to decide if it's productive.

Simply editing the question is permitted. If I'm unsure of the best way to pose the question I specifically note that "Improvements to the question are welcomed". If it's a good question that's going to help a number of people in the future it's worth putting some effort into it. If it's "unclear what is being asked" there's a flag for that.

Go in knowing what your commitment is going to be and don't go far beyond it. If I only have a few minutes available I don't tackle a question that will need a long answer.

How one can recommend the user edit their question in order to avoid this from happening?

Just ask, or you do it (regardless of rep, it can be reviewed by peers). Great Q&A is what this site wants. It is sometimes tough to know the correct way to phrase a question when you don't know the answer, even harder to answer when the asker doesn't know the question.

Give them the benefit of the doubt, commit sufficiently, don't get discouraged or stuck in a loop that slowly leads nowhere. Work for the greater good, if the asker (or answerer) becomes enough of a nuisance they'll accumulate some downvotes to guide them on their way.

Some people don't so much want to play "cat and mouse", instead they feel entitled to play "50! questions"; but if they told you that upfront you might not be interested. They need you to debug their thought processes.

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